Question

Find f^-1(x) given that f(x) = 3x²+1

Answer 1

`f^(-1)(x)=\sqrt[]{(x-1)/(3)}`

Step-by-step explanation:

Given the function:

`f(x)=3x^2+1`

To find the inverse function, follow the steps below:

Step 1: Replace f(x) with y

`y=3x^2+1`

Step 2: Swap x and y.

`x=3y^2+1`

Step 3: Make y the subject:

`\begin{gathered} 3y^2=x-1 \\ y^2=(x-1)/(3) \\ y=\sqrt[]{(x-1)/(3)} \end{gathered}`

Step 4: Replace y with the inverse function.

`f^(-1)(x)=\sqrt[]{(x-1)/(3)}`